Assuming monotonicity of \(\Lambda \)  is not an abstract condition.
In many cases (e.g. in the linear quadratic case) \(\Lambda \)  is a linear function of \(y\) .
Note moreover that by (REF ) the function \(\Lambda \)  is Lipschitz–continuous (see e.g. [1]}).
Let us denote by \(L_\Lambda \)  its Lipschitz constant.
Under the above additional assumption, we have the following LDP:
